Source code for firedrake.norms

from ufl import inner, div, grad, curl, dx

from firedrake.assemble import assemble
from firedrake import function
from firedrake.logging import warning

__all__ = ['errornorm', 'norm']

[docs]def errornorm(u, uh, norm_type="L2", degree_rise=None, mesh=None): """Compute the error :math:`e = u - u_h` in the specified norm. :arg u: a :class:`.Function` or UFL expression containing an "exact" solution :arg uh: a :class:`.Function` containing the approximate solution :arg norm_type: the type of norm to compute, see :func:`.norm` for details of supported norm types. :arg degree_rise: ignored. :arg mesh: an optional mesh on which to compute the error norm (currently ignored). """ urank = len(u.ufl_shape) uhrank = len(uh.ufl_shape) if urank != uhrank: raise RuntimeError("Mismatching rank between u and uh") if not isinstance(uh, function.Function): raise ValueError("uh should be a Function, is a %r", type(uh)) if isinstance(u, function.Function): degree_u = u.function_space().ufl_element().degree() degree_uh = uh.function_space().ufl_element().degree() if degree_uh > degree_u: warning("Degree of exact solution less than approximation degree") return norm(u - uh, norm_type=norm_type, mesh=mesh)
[docs]def norm(v, norm_type="L2", mesh=None): r"""Compute the norm of ``v``. :arg v: a ufl expression (:class:`~.ufl.classes.Expr`) to compute the norm of :arg norm_type: the type of norm to compute, see below for options. :arg mesh: an optional mesh on which to compute the norm (currently ignored). Available norm types are: - Lp :math:`||v||_{L^p} = (\int |v|^p)^{\frac{1}{p}} \mathrm{d}x` - H1 :math:`||v||_{H^1}^2 = \int (v, v) + (\nabla v, \nabla v) \mathrm{d}x` - Hdiv :math:`||v||_{H_\mathrm{div}}^2 = \int (v, v) + (\nabla\cdot v, \nabla \cdot v) \mathrm{d}x` - Hcurl :math:`||v||_{H_\mathrm{curl}}^2 = \int (v, v) + (\nabla \wedge v, \nabla \wedge v) \mathrm{d}x` """ typ = norm_type.lower() p = 2 if typ == 'l2': expr = inner(v, v) elif typ.startswith('l'): try: p = int(typ[1:]) if p < 1: raise ValueError except ValueError: raise ValueError("Don't know how to interpret %s-norm" % norm_type) expr = inner(v, v) elif typ == 'h1': expr = inner(v, v) + inner(grad(v), grad(v)) elif typ == "hdiv": expr = inner(v, v) + div(v)*div(v) elif typ == "hcurl": expr = inner(v, v) + inner(curl(v), curl(v)) else: raise RuntimeError("Unknown norm type '%s'" % norm_type) return assemble((expr**(p/2))*dx)**(1/p)